WEEK 5 ASSIGNMENT .docx - a. Formulate the problem as a...

a. Formulate the problem as a linear program, with the optimal solution providing the hours each
consultant should be scheduled for each client to maximize the consulting firm’s billings. What is the
schedule and what is the total billing?
.
M
ax
100
x
11
+
125
x
12
+
115
x
13
+
100
x
14
+
120
x
21
+
135
x
22
+
115
x
23
+
120
x
24
+
155
x
31
+
150
x
32
+
140
x
33
+
130
x
34
s.t
.
1 x
11
+
1 x
12
+
1 x
13
+
1 x
14
≤
16
0
1 x
21
+
1 x
22
+
1 x
23
+
1 x
24
≤
16
0
1 x
31
+
1 x
32
+
1 x
33
+
1
x
34
≤
14
0
1 x
11
+
1 x
21
+
1 x
31
=
18
0
1 x
12
+
1 x
22
+
1 x
32
= 75
1 x
13
+
1 x
23
+
1 x
33
=
10
0
1 x
14
+
1 x
24
+
1
x
34
= 85
x
ij
≥ 0 for all i , j
b.
Hours Assigned Billing
Avery-Client A 0 $ 0
Avery-Client B 40 5000
Avery-Client C 100 11500
Avery-Client D 0 0
Baker-Client A 40 4800
Baker-Client B 35 4725
Baker-Client C 0 0
Baker-Client D 85 10200
Campbell-Client A 140 21700
Campbell-Client B 0 0
Campbell-Client C 0 0
Campbell-Client D 0 0

Total Billing $ 57925
d.
e. New information shows that Avery doesn’t have the experience to be scheduled for client B. If
this consulting assignment is not permitted, what impact does it have on total billings? What is the
revised schedule?
Hours Assigned Billing
Avery-Client A 40 $ 4000
Avery-Client B 0 0
Avery-Client C 100 11500
Avery-Client D 0 0
Baker-Client A 0 0
Baker-Client B 75 10125
Baker-Client C 0 0
Baker-Client D 85 10200
Campbell-Client A 140 21700
Campbell-Client B 0 0
Campbell-Client C 0 0
Campbell-Client D 0 0
Total Billing $ 57525

Chapter Introduction
Problem 10-07 (Algorithmic)
Aggie Power Generation supplies electrical power to residential customers for many U.S. cities. Its
main power generation plants are located in Los Angeles, Tulsa, and Seattle. The following table shows
Aggie Power Generation's major residential markets, the annual demand in each market (in megawatts
or MWs), and the cost to supply electricity to each market from each power generation plant (prices
are in $/MW).
Distribution Costs
City Los Angeles Tulsa Seattle Demand (MWs)
Seattle $348.25 $585.75 $51.38 942.00
Portland $380.25 $617.75 $202.13 855.25
San Francisco $157.13 $454.00 $275.88 2354.00
Boise $357.25 $476.00 $297.88 594.75
Reno $222.50 $460.00 $341.25 935.00
Bozeman $442.63 $442.63 $323.88 520.15
Laramie $380.25 $439.63 $380.25 1211.50
Park City $377.25 $377.25 $496.00 624.25